The present invention relates to a function variable value transmitter, a function receiver and respective systems made up of the same, such as sensor networks.
Modern wireless “sensor networks” consists of a very large number of inexpensive assemblies or sensor nodes which are interconnected via a wireless communication interface. Due to the wireless network aspect, the same differ significantly from a mere assembly of sensors, since the associated capabilities regarding cooperation, coordination and collaboration extremely broaden the radius of application.
Compared to conventional data networks, such as the internet, whose primary object is to provide an end-to-end information traffic, sensor networks are usually extremely application-specific, which means that the same are explicitly developed and used for fulfilling specific tasks. Examples for this are, exemplarily, surroundings monitoring, monitoring of physical phenomenons, building security, quality control, etc. Compared to the above-mentioned conventional data networks, this application driven characteristics of wireless sense networks necessitates completely new design paradigms.
In many sensor network applications, a unique receiving node (access point) sometimes also referred to as collecting node or central processing unit is not interested in reconstructing the individual measurement values of the nodes within the network, but is frequently interested in a desired function ƒ which depends, linearly or non-linearly, either on the entirety of all measurement values or on a specific subset. Desired functions can be, for example, the arithmetic average, the geometric average, the maximum measurement value, the minimum measurement value, the harmonic average, a weighted sum of the measurement data, a number of sensor nodes that are active within the network, etc.
Thus, it would be desirable to calculate desired linear and nonlinear functions in wireless sensor networks with as little energy expenditure as possible for increased network lifetime, heavily reduced complexity, as little coordination as possible and with simple implementation effort.
In other words, the problem is to transmit function variable values resulting at function variable value transmitters as effectively as possible to a function receiver. Based on FIG. 1, the problem will be illustrated again. FIG. 1 shows exemplarily a sensor network with sensor nodes 101, 102, 103, . . . , 10k, 10k+1, . . . . , 10K as well as a receiving node 12. According to the sensor network example of FIG. 1, the K sensor nodes 101 . . . 10K are spatially arranged around the indicated receiving node 12 in a distributed manner. It is the object of the sensor network to reliably calculate the function ƒ(X1(t), . . . , XK(t)) at the location of the receiving node, wherein X1(t), . . . , XK(t) represent the values of the individual sensors measured at the time t.
In order to adequately solve the problem of function value computation, it is possible to strictly separate the processes of “measurement value transmission” or transmission of function variable values to the receiver on the one hand and “function value computation” on the other hand in the wireless sensor network of FIG. 1. This means that every sensor node 101 . . . 10K would transmit its measurement values information for example in a quantized manner and separately as digital bitstream to the receiving node 12. The same would then reconstruct the respective measurement value from the individual receive signals and would subsequently calculate the desired function, for example in an internally existing microprocessor.
The inherent characteristic of every wireless channel is, however, the occurrence of interference as soon as different users simultaneously access common resources, such as bandwidth and/or transmission time. A separation of the signals at the receiving node can normally only be realized with high effort or is not possible at all. For accommodating these circumstances, in wireless sense networks as the one in FIG. 1, it is possible to use “orthogonalizing” methods, such as TDMA (Time Division Multiple Access), according to which a specific transmission time could be allocated to every individual sensor node 101-10K, in which the existing resources can exclusively be used by the same. It is obvious that such an approach necessitates a high degree of coordination, in order to ensure that every node 101-10K is addressed, is informed when it is assigned what time slot, etc. The coordination would have to be taken on by a specific protocol structure which would provide for the allocation and time synchronization by respective additional effort, such as signalizing messages, acknowledgement signals, etc. However, such a procedure significantly reduces the flexibility and life time of a sensor network and is hence extremely suboptimal in the context of function value computation. Additionally, the transmission characteristics of wireless channels can be subject to severe time-dependent variations, also referred to as fading, which necessitate channel estimation at the respective signal receiver or even at the signal transmitter itself to enable adequate and reliable signal transmission. This procedure causes additional effort and associated therewith obviously also significant energy consumption which has an essential influence on the network lifetime, especially in sensor networks having a large number of nodes.
A further disadvantage of the strict separation between function variable value transmission according to TDMA on the one hand and actual function result computation on the other hand is the extremely limited data rate with regard to function value computation. This means that with uniform quantization of each of the K measurement values with Q bits, the receiving nodes can calculate a function value of the reconstructed data every Q·K time slots at most, which is why especially for large networks where K is large and/or in the case of a fine resolution, i.e. Q is large, the waiting cycles are significant. When a specific protocol structure exists, such as IEEE Standard 802.15.4, even (Q+R)K time slots are necessitated, wherein R describes the number of bits induced by the overhead of the protocol in every time slot. Consequently, the receiving node can request a new function value only every (Q+R)K time slots, which is a very limiting factor, especially in time critical applications or alarm situations.
Information-theoretical analyses in B. Nazer and M. Gastpar, “Computation over multiple-access channels,” IEEE Trans. Inf. Theory, Vol. 53, No. 10, P. 3498-3516, October 2007 have shown, however, that when strictly assuming perfect synchronization and perfect channel information at sensor nodes, the interference characteristic of multiple-access channels can explicitly be used for calculating linear functions. In particular, this reference suggests to simultaneously transmit digital function variable values bit by bit or digit by digit to the receiving node, and to thereby incorporate the characteristics of the multiple-access channel in the interesting computation of the linear combination of the function variable values. The inherent characteristic or the mathematical behavior of the multiple-access channel, which is used there, consists of forming a linear combination or summation of the simultaneously transmitted complex-valued transmitting symbols Rkq(t), k=1, . . . , K; q=1, . . . , Q, which resulted from measurement data Xk(t) by quantizing, i.e. Q(Xk(t))=(Rk1(t), . . . , RkQ(t)) for all k, wherein Q describes any abstract quantization operator. The output of the wireless multiple-access channel, when assuming perfect synchronization between sensor nodes, has the explicit form:
                                                        Y              q                        ⁡                          (              t              )                                =                                                    ∑                                  k                  =                  1                                K                            ⁢                                                          ⁢                                                                    H                    kq                                    ⁡                                      (                    t                    )                                                  ⁢                                                      R                    kq                                    ⁡                                      (                    t                    )                                                                        +                                          N                q                            ⁡                              (                t                )                                                    ,                                  ⁢                  q          =          1                ,        …        ⁢                                  ,        Q        ,                            (        1        )            wherein Hkq(t) describes the complex channel influence (fading coefficient) between the kth sensor and the receiving node during transmission of the qth symbol and Nq(t) designates complex additive receiver noise. Equation (1) specifies again mathematically the above-mentioned behavior of the multiple-access channel, namely formation of a linear combination (summation). Here, it should be noted that q represents a discrete time parameter not to be mistaken for the excitation time t.
Thus, the idea of Nazer and Gastpar uses the sum characteristic (1) for calculating linear functions under the condition of a certain correspondence between the behavior of the multiple-access channel (1) and the desired function ƒ(X1(t) . . . , XK(t)). Since in this context no steps have to be taken against the interference influence of the channel, in the ideal case and in contrast to the TDMA example described above, a new function value can be initiated from the access point every Q time slots.
However, the purely information-theoretical considerations of Nazer and Gastpar have a significant disadvantage, namely the assumption of perfect synchronization between sensor nodes, which can, especially in large networks, not be realized at all or only with unreasonably large effort. Thus, in M. Goldenbaum, S. Stanczak and M. Kaliszan, “On function computation via wireless sensor multiple-access channels,” in Proc. IEEE Wireless Communications & Networking Conference (WCNC), Budapest, Hungary, April 2009 a method has been presented which can do completely without explicit protocol structure and additionally makes only coarse synchronization requests to the system. In contrast to Nazer and Gastpar, the idea of the latter article was to let every sensor node transmit a different sequence of complex values of the length MεN with a transmit power that depends on the measured sensor data. Under certain conditions, the powers of the K sequences add up during transmission via the multiple-access channel, so that all the receiving node has to do is merely determine the receive power and to perform some simple arithmetic computations. For implementation, it is suggested to use, as the sequences of complex values whose transmit power is set according to the function variable value to be transmitted, unit norm sequences of random phases having a constant magnitude. Thus, synchronization is significantly less critical than for Nazer and Gastpar. However, this approach also assumes perfect knowledge of complex channel coefficients describing the channel influence between the respective sensor node and the receiving node. Thus, although the synchronization tasks are less critical than for Nazer and Gastpar, even according to the latter approach, there remains the high effort for perfect estimation of the complex channel influence between transmitters and receivers, and this influence shows in increased power costs for channel estimation as well as in a reduced function result rate.